What happens to game achievements if you play offline without Gog Galaxy in the background?
Do they update the next time you launch the game via the client?

If you're not using Galaxy when you trigger the event for the achievement, I do not believe you receive it when you log in. Galaxy doesn't see the flag, and you miss the achievement(s).

At least, this was Galaxy's behavior last time I tested it, which was about a year ago.

Sorry for the late reply but thank you. That answered my question.

np :)

CymTyr might be right, but beware that many many games take a different approach on achievements.

We might think that the call to unlock the achievement is made ONLY at the time the achievement is unlocked, but that in many cases it's not true, because this approach would be prone to lots of issues.

Imagine playing the game, you got to unlock the achievement but unfortunately, you were playing a little bit too far from your wifi range and you got disconnected for few seconds and BOOM you lost your achievement.

Instead, many games just record you got the achievement in your save file. Then, on many occasions (eg. loading the save, on a scheduled timer, ...) the game goes through your locally recorded achievements and checks if they really got unlocked or not. If the latter, it issues another unlock request to the server.

This being said, I don't know how this game handles this matter, but just for you to know. There are many games in which offline achievements will work once you get back online and the game is fired up. What is true for sure, btw, is this. If you don't launch games via GOG Galaxy, the game cannot access your account, and obviously the entire GOG integrations (achievements included) get disabled. Not launching games via Galaxy is a 90% sure way to not getting your achievements unlocked.

Cheers